The Heroic Century

Abstract

The theory of differentiation and integration is called infinitesimal calculus, which means computation with infinitely small entities. It dates from the seventeenth century, which saw the birth of modern mathematics. For some time the strict proofs of the Greeks had been abandoned in favor of heuristic reasoning. Audaciously exploring new approaches, mathematicians surpassed everything that had been done before. The century had long religious wars, severe crop failures, and serious outbreaks of the plague, but for science and mathematics it was a time of unprecedented discoveries. The development was rapid. The works of Galilei (from 1604) on accelerated motion are almost childish compared to what Leibniz and the brothers Bernoulli did at the end of the century, solving many different problems of infinitesimal calculus and variational calculus with modern methods and notation.